Unsupervised Learning: Trade&Ahead - Jason Giust

Marks: 60

Context

The stock market has consistently proven to be a good place to invest in and save for the future. There are a lot of compelling reasons to invest in stocks. It can help in fighting inflation, create wealth, and also provides some tax benefits. Good steady returns on investments over a long period of time can also grow a lot more than seems possible. Also, thanks to the power of compound interest, the earlier one starts investing, the larger the corpus one can have for retirement. Overall, investing in stocks can help meet life's financial aspirations.

It is important to maintain a diversified portfolio when investing in stocks in order to maximise earnings under any market condition. Having a diversified portfolio tends to yield higher returns and face lower risk by tempering potential losses when the market is down. It is often easy to get lost in a sea of financial metrics to analyze while determining the worth of a stock, and doing the same for a multitude of stocks to identify the right picks for an individual can be a tedious task. By doing a cluster analysis, one can identify stocks that exhibit similar characteristics and ones which exhibit minimum correlation. This will help investors better analyze stocks across different market segments and help protect against risks that could make the portfolio vulnerable to losses.

Objective

Trade&Ahead is a financial consultancy firm who provide their customers with personalized investment strategies. They have hired you as a Data Scientist and provided you with data comprising stock price and some financial indicators for a few companies listed under the New York Stock Exchange. They have assigned you the tasks of analyzing the data, grouping the stocks based on the attributes provided, and sharing insights about the characteristics of each group.

Data Dictionary

• Ticker Symbol: An abbreviation used to uniquely identify publicly traded shares of a particular stock on a particular stock market
• Company: Name of the company
• GICS Sector: The specific economic sector assigned to a company by the Global Industry Classification Standard (GICS) that best defines its business operations
• GICS Sub Industry: The specific sub-industry group assigned to a company by the Global Industry Classification Standard (GICS) that best defines its business operations
• Current Price: Current stock price in dollars
• Price Change: Percentage change in the stock price in 13 weeks
• Volatility: Standard deviation of the stock price over the past 13 weeks
• ROE: A measure of financial performance calculated by dividing net income by shareholders' equity (shareholders' equity is equal to a company's assets minus its debt)
• Cash Ratio: The ratio of a company's total reserves of cash and cash equivalents to its total current liabilities
• Net Cash Flow: The difference between a company's cash inflows and outflows (in dollars)
• Net Income: Revenues minus expenses, interest, and taxes (in dollars)
• Earnings Per Share: Company's net profit divided by the number of common shares it has outstanding (in dollars)
• Estimated Shares Outstanding: Company's stock currently held by all its shareholders
• P/E Ratio: Ratio of the company's current stock price to the earnings per share
• P/B Ratio: Ratio of the company's stock price per share by its book value per share (book value of a company is the net difference between that company's total assets and total liabilities)

Importing necessary libraries and data

# this will help in making the Python code more structured automatically (good coding practice)
%load_ext nb_black

# Libraries to help with reading and manipulating data
import numpy as np
import pandas as pd

# Libraries to help with data visualization
import matplotlib.pyplot as plt
import seaborn as sns

# Removes the limit for the number of displayed columns
pd.set_option("display.max_columns", None)
# Sets the limit for the number of displayed rows
pd.set_option("display.max_rows", 200)

# to scale the data using z-score
from sklearn.preprocessing import StandardScaler

# to compute distances
from scipy.spatial.distance import pdist, cdist

# to perform hierarchical clustering, compute cophenetic correlation, and create dendrograms
from sklearn.cluster import AgglomerativeClustering
from scipy.cluster.hierarchy import dendrogram, linkage, cophenet

# to perform PCA
from sklearn.decomposition import PCA

# to perform k-means clustering and compute silhouette scores
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score

# to visualize the elbow curve and silhouette scores
from yellowbrick.cluster import KElbowVisualizer, SilhouetteVisualizer

# to suppress warnings
import warnings

warnings.filterwarnings("ignore")

Data Overview

• Observations
• Sanity checks

data = pd.read_csv("stock_data.csv")

data.shape

(340, 15)

Exploratory Data Analysis (EDA)

• EDA is an important part of any project involving data.
• It is important to investigate and understand the data better before building a model with it.
• A few questions have been mentioned below which will help you approach the analysis in the right manner and generate insights from the data.
• A thorough analysis of the data, in addition to the questions mentioned below, should be done.

Questions:

1. What does the distribution of stock prices look like?
2. The stocks of which economic sector have seen the maximum price increase on average?
3. How are the different variables correlated with each other?
4. Cash ratio provides a measure of a company's ability to cover its short-term obligations using only cash and cash equivalents. How does the average cash ratio vary across economic sectors?
5. P/E ratios can help determine the relative value of a company's shares as they signify the amount of money an investor is willing to invest in a single share of a company per dollar of its earnings. How does the P/E ratio vary, on average, across economic sectors?

Data Preprocessing

• Duplicate value check
• Missing value treatment
• Outlier check
• Feature engineering (if needed)
• Any other preprocessing steps (if needed)

# copying data set to avoid making unintended changes to the original data
df = data.copy()

df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 340 entries, 0 to 339
Data columns (total 15 columns):
 #   Column                        Non-Null Count  Dtype  
---  ------                        --------------  -----  
 0   Ticker Symbol                 340 non-null    object 
 1   Security                      340 non-null    object 
 2   GICS Sector                   340 non-null    object 
 3   GICS Sub Industry             340 non-null    object 
 4   Current Price                 340 non-null    float64
 5   Price Change                  340 non-null    float64
 6   Volatility                    340 non-null    float64
 7   ROE                           340 non-null    int64  
 8   Cash Ratio                    340 non-null    int64  
 9   Net Cash Flow                 340 non-null    int64  
 10  Net Income                    340 non-null    int64  
 11  Earnings Per Share            340 non-null    float64
 12  Estimated Shares Outstanding  340 non-null    float64
 13  P/E Ratio                     340 non-null    float64
 14  P/B Ratio                     340 non-null    float64
dtypes: float64(7), int64(4), object(4)
memory usage: 40.0+ KB

• some object data types that will be converted to categorical.

# checking for duplicate values
df.duplicated().sum()

0

• No duplicates.

# checking for missing values
df.isnull().sum()

Ticker Symbol                   0
Security                        0
GICS Sector                     0
GICS Sub Industry               0
Current Price                   0
Price Change                    0
Volatility                      0
ROE                             0
Cash Ratio                      0
Net Cash Flow                   0
Net Income                      0
Earnings Per Share              0
Estimated Shares Outstanding    0
P/E Ratio                       0
P/B Ratio                       0
dtype: int64

• No missing values.

EDA

• It is a good idea to explore the data once again after manipulating it.

# check the statistical summary of the data.
df.describe(include="all").T

	count	unique	top	freq	mean	std	min	25%	50%	75%	max
Ticker Symbol	340	340	AAL	1	NaN	NaN	NaN	NaN	NaN	NaN	NaN
Security	340	340	American Airlines Group	1	NaN	NaN	NaN	NaN	NaN	NaN	NaN
GICS Sector	340	11	Industrials	53	NaN	NaN	NaN	NaN	NaN	NaN	NaN
GICS Sub Industry	340	104	Oil & Gas Exploration & Production	16	NaN	NaN	NaN	NaN	NaN	NaN	NaN
Current Price	340.0	NaN	NaN	NaN	80.862345	98.055086	4.5	38.555	59.705	92.880001	1274.949951
Price Change	340.0	NaN	NaN	NaN	4.078194	12.006338	-47.129693	-0.939484	4.819505	10.695493	55.051683
Volatility	340.0	NaN	NaN	NaN	1.525976	0.591798	0.733163	1.134878	1.385593	1.695549	4.580042
ROE	340.0	NaN	NaN	NaN	39.597059	96.547538	1.0	9.75	15.0	27.0	917.0
Cash Ratio	340.0	NaN	NaN	NaN	70.023529	90.421331	0.0	18.0	47.0	99.0	958.0
Net Cash Flow	340.0	NaN	NaN	NaN	55537620.588235	1946365312.175789	-11208000000.0	-193906500.0	2098000.0	169810750.0	20764000000.0
Net Income	340.0	NaN	NaN	NaN	1494384602.941176	3940150279.327937	-23528000000.0	352301250.0	707336000.0	1899000000.0	24442000000.0
Earnings Per Share	340.0	NaN	NaN	NaN	2.776662	6.587779	-61.2	1.5575	2.895	4.62	50.09
Estimated Shares Outstanding	340.0	NaN	NaN	NaN	577028337.754029	845849595.417695	27672156.86	158848216.1	309675137.8	573117457.325	6159292035.0
P/E Ratio	340.0	NaN	NaN	NaN	32.612563	44.348731	2.935451	15.044653	20.819876	31.764755	528.039074
P/B Ratio	340.0	NaN	NaN	NaN	-1.718249	13.966912	-76.119077	-4.352056	-1.06717	3.917066	129.064585

Univariate Analysis

# function to plot a boxplot and a histogram along the same scale.


def histogram_boxplot(data, feature, figsize=(12, 7), kde=False, bins=None):
    """
    Boxplot and histogram combined

    data: dataframe
    feature: dataframe column
    figsize: size of figure (default (12,7))
    kde: whether to the show density curve (default False)
    bins: number of bins for histogram (default None)
    """
    f2, (ax_box2, ax_hist2) = plt.subplots(
        nrows=2,  # Number of rows of the subplot grid= 2
        sharex=True,  # x-axis will be shared among all subplots
        gridspec_kw={"height_ratios": (0.25, 0.75)},
        figsize=figsize,
    )  # creating the 2 subplots
    sns.boxplot(
        data=data, x=feature, ax=ax_box2, showmeans=True, color="violet"
    )  # boxplot will be created and a star will indicate the mean value of the column
    sns.histplot(
        data=data, x=feature, kde=kde, ax=ax_hist2, bins=bins, palette="winter"
    ) if bins else sns.histplot(
        data=data, x=feature, kde=kde, ax=ax_hist2
    )  # For histogram
    ax_hist2.axvline(
        data[feature].mean(), color="green", linestyle="--"
    )  # Add mean to the histogram
    ax_hist2.axvline(
        data[feature].median(), color="black", linestyle="-"
    )  # Add median to the histogram

1. What does the distribution of stock prices look like?

histogram_boxplot(df, "Current Price")

• Most stock prices are under $200.
• Right skewed due to some very large values.

2. The stocks of which economic sector have seen the maximum price increase on average?

• The Health Care sector has seen the largest increase in price on average.

histogram_boxplot(df, "Price Change")

• The distribution of Price Change is approximately normal.

histogram_boxplot(df, "Volatility")

• Volatility is skewed right containing outliers, but mostly normal.

histogram_boxplot(df, "ROE")

• ROE is approximately normal with some outliers.

histogram_boxplot(df, "Cash Ratio")

• Very few companies have a Cash Ratio higher than 200.

histogram_boxplot(df, "Net Cash Flow")

• Net Cash Flow is approximately normal with some large outliers on both sides of the distribution.

histogram_boxplot(df, "Net Income")

• The distribution of Net Income is approximatley normal.

histogram_boxplot(df, "Earnings Per Share")

• Earnings Per Share are mostly positive between 0 - $10.

histogram_boxplot(df, "Estimated Shares Outstanding")

• Most companies have less than 1B shares outstanding.

histogram_boxplot(df, "P/E Ratio")

• P/E Ratio is right skewed with most companies below 100.

histogram_boxplot(df, "P/B Ratio")

• The distribution of P/B Ratio is mostly normal.

# function to create labeled barplots


def labeled_barplot(data, feature, perc=False, n=None):
    """
    Barplot with percentage at the top

    data: dataframe
    feature: dataframe column
    perc: whether to display percentages instead of count (default is False)
    n: displays the top n category levels (default is None, i.e., display all levels)
    """

    total = len(data[feature])  # length of the column
    count = data[feature].nunique()
    if n is None:
        plt.figure(figsize=(count + 1, 5))
    else:
        plt.figure(figsize=(n + 1, 5))

    plt.xticks(rotation=90, fontsize=15)
    ax = sns.countplot(
        data=data,
        x=feature,
        palette="Paired",
        order=data[feature].value_counts().index[:n].sort_values(),
    )

    for p in ax.patches:
        if perc == True:
            label = "{:.1f}%".format(
                100 * p.get_height() / total
            )  # percentage of each class of the category
        else:
            label = p.get_height()  # count of each level of the category

        x = p.get_x() + p.get_width() / 2  # width of the plot
        y = p.get_height()  # height of the plot

        ax.annotate(
            label,
            (x, y),
            ha="center",
            va="center",
            size=12,
            xytext=(0, 5),
            textcoords="offset points",
        )  # annotate the percentage

    plt.show()  # show the plot

labeled_barplot(df, "GICS Sector", perc=True)

• The top four sectors are Industrials, Financials, Consumer Discretionary, and Health Care.

4. Cash ratio provides a measure of a company's ability to cover its short-term obligations using only cash and cash equivalents. How does the average cash ratio vary across economic sectors?

plt.figure(figsize=(10, 5))
sns.barplot(data=df, x="GICS Sector", y="Cash Ratio", ci=False)
plt.xticks(rotation=90)
plt.show()

• Cash ratio ranges from 15 to as high as 150.
• On average it appears to be about 60 across economic sectors.

5. P/E ratios can help determine the relative value of a company's shares as they signify the amount of money an investor is willing to invest in a single share of a company per dollar of its earnings. How does the P/E ratio vary, on average, across economic sectors?

plt.figure(figsize=(10, 5))
sns.barplot(data=df, x="GICS Sector", y="P/E Ratio", ci=False)
plt.xticks(rotation=90)
plt.show()

• P/E Ratios range from approximately 12 to as high as 75.
• On average, the P/E Ratios are about 20 across economic sectors.

labeled_barplot(df, "GICS Sub Industry", perc=True, n=15)

• The top four sub industries are Oil & Gas Exploration & Production, Industrial Conglomerates, Electric Utilities, and Internet Software & Services.

Bivariate Analysis

Let's check for correlations

num_col = [
    "Current Price",
    "Price Change",
    "Volatility",
    "ROE",
    "Cash Ratio",
    "Net Cash Flow",
    "Net Income",
    "Earnings Per Share",
    "Estimated Shares Outstanding",
    "P/E Ratio",
    "P/B Ratio",
]

3. How are the different variables correlated with each other?

plt.figure(figsize=(15, 7))
sns.heatmap(df[num_col].corr(), annot=True, vmin=-1, vmax=1, fmt=".2f", cmap="Spectral")
plt.show()

sns.pairplot(data=df[num_col], diag_kind="kde")
plt.show()

Outliers

plt.figure(figsize=(15, 12))

numeric_columns = df.select_dtypes(include=np.number).columns.tolist()

for i, variable in enumerate(numeric_columns):
    plt.subplot(3, 4, i + 1)
    plt.boxplot(df[variable], whis=1.5)
    plt.tight_layout()
    plt.title(variable)

plt.show()

• There are outliers in each of the data sets. They are proper values, so we will not treat them.

K-means Clustering

# Scaling the data set before clustering
scaler = StandardScaler()
subset = df[num_col].copy()
subset_scaled = scaler.fit_transform(subset)

# Creating a dataframe from the scaled data
subset_scaled_df = pd.DataFrame(subset_scaled, columns=subset.columns)

clusters = range(1, 10)
meanDistortions = []

for k in clusters:
    model = KMeans(n_clusters=k)
    model.fit(subset_scaled_df)
    prediction = model.predict(subset_scaled_df)
    distortion = (
        sum(
            np.min(cdist(subset_scaled_df, model.cluster_centers_, "euclidean"), axis=1)
        )
        / subset_scaled_df.shape[0]
    )

    meanDistortions.append(distortion)

    print("Number of Clusters:", k, "\tAverage Distortion:", distortion)

plt.plot(clusters, meanDistortions, "bx-")
plt.xlabel("k")
plt.ylabel("Average Distortion")
plt.title("Selecting k with the Elbow Method", fontsize=20)

Number of Clusters: 1 	Average Distortion: 2.5425069919221697
Number of Clusters: 2 	Average Distortion: 2.382318498894466
Number of Clusters: 3 	Average Distortion: 2.2683105560042285
Number of Clusters: 4 	Average Distortion: 2.1804670329624374
Number of Clusters: 5 	Average Distortion: 2.123228143152355
Number of Clusters: 6 	Average Distortion: 2.053350668955699
Number of Clusters: 7 	Average Distortion: 2.0312771801534404
Number of Clusters: 8 	Average Distortion: 1.9667200710989037
Number of Clusters: 9 	Average Distortion: 1.9609293600576212

Text(0.5, 1.0, 'Selecting k with the Elbow Method')

• The appropriate value of k from the elbow curve appears to be 4 or 5.

model = KMeans(random_state=1)
visualizer = KElbowVisualizer(model, k=(1, 10), timings=True)
visualizer.fit(subset_scaled_df)  # fit the data to the visualizer
visualizer.show()  # finalize and render figure

<AxesSubplot:title={'center':'Distortion Score Elbow for KMeans Clustering'}, xlabel='k', ylabel='distortion score'>

Let's check the silhouette scores

sil_score = []
cluster_list = list(range(2, 10))
for n_clusters in cluster_list:
    clusterer = KMeans(n_clusters=n_clusters)
    preds = clusterer.fit_predict((subset_scaled_df))
    # centers = clusterer.cluster_centers_
    score = silhouette_score(subset_scaled_df, preds)
    sil_score.append(score)
    print("For n_clusters = {}, silhouette score is {}".format(n_clusters, score))

plt.plot(cluster_list, sil_score)

For n_clusters = 2, silhouette score is 0.43969639509980457
For n_clusters = 3, silhouette score is 0.4576529285895266
For n_clusters = 4, silhouette score is 0.4514969925542859
For n_clusters = 5, silhouette score is 0.4431884406997652
For n_clusters = 6, silhouette score is 0.43585057251228676
For n_clusters = 7, silhouette score is 0.39397699902210176
For n_clusters = 8, silhouette score is 0.42849009921450093
For n_clusters = 9, silhouette score is 0.38352786568064534

[<matplotlib.lines.Line2D at 0x21aaa65b8e0>]

• The silhouette score for 4 is higher than 5. So, we will choose 4 as the value of k.

model = KMeans(random_state=1)
visualizer = KElbowVisualizer(model, k=(2, 15), metric="silhouette", timings=True)
visualizer.fit(subset_scaled_df)  # fit the data to the visualizer
visualizer.show()  # finalize and render figure

<AxesSubplot:title={'center':'Silhouette Score Elbow for KMeans Clustering'}, xlabel='k', ylabel='silhouette score'>

# finding optimal no. of clusters with silhouette coefficients
visualizer = SilhouetteVisualizer(KMeans(2, random_state=1))
visualizer.fit(subset_scaled_df)
visualizer.show()

<AxesSubplot:title={'center':'Silhouette Plot of KMeans Clustering for 340 Samples in 2 Centers'}, xlabel='silhouette coefficient values', ylabel='cluster label'>

# finding optimal no. of clusters with silhouette coefficients
visualizer = SilhouetteVisualizer(KMeans(3, random_state=1))
visualizer.fit(subset_scaled_df)
visualizer.show()

<AxesSubplot:title={'center':'Silhouette Plot of KMeans Clustering for 340 Samples in 3 Centers'}, xlabel='silhouette coefficient values', ylabel='cluster label'>

# finding optimal no. of clusters with silhouette coefficients
visualizer = SilhouetteVisualizer(KMeans(4, random_state=1))
visualizer.fit(subset_scaled_df)
visualizer.show()

<AxesSubplot:title={'center':'Silhouette Plot of KMeans Clustering for 340 Samples in 4 Centers'}, xlabel='silhouette coefficient values', ylabel='cluster label'>

# finding optimal no. of clusters with silhouette coefficients
visualizer = SilhouetteVisualizer(KMeans(5, random_state=1))
visualizer.fit(subset_scaled_df)
visualizer.show()

<AxesSubplot:title={'center':'Silhouette Plot of KMeans Clustering for 340 Samples in 5 Centers'}, xlabel='silhouette coefficient values', ylabel='cluster label'>

# finding optimal no. of clusters with silhouette coefficients
visualizer = SilhouetteVisualizer(KMeans(6, random_state=1))
visualizer.fit(subset_scaled_df)
visualizer.show()

<AxesSubplot:title={'center':'Silhouette Plot of KMeans Clustering for 340 Samples in 6 Centers'}, xlabel='silhouette coefficient values', ylabel='cluster label'>

Selecting final model

Let's take 4 as the appropriate no. of clusters as the silhouette score is high enough and there is knick at 4 in the elbow curve.

kmeans = KMeans(n_clusters=4, random_state=1)
kmeans.fit(subset_scaled_df)

KMeans(n_clusters=4, random_state=1)

# adding kmeans cluster labels to the original dataframe and scaled dataframe
subset_scaled_df["K_means_segments"] = kmeans.labels_
df["K_means_segments"] = kmeans.labels_

Cluster Profiling

cluster_profile = df.groupby("K_means_segments").mean()

cluster_profile["count_in_each_segment"] = (
    df.groupby("K_means_segments")["Security"].count().values
)

# let's display cluster profiles
cluster_profile.style.highlight_max(color="lightgreen", axis=0)

	Current Price	Price Change	Volatility	ROE	Cash Ratio	Net Cash Flow	Net Income	Earnings Per Share	Estimated Shares Outstanding	P/E Ratio	P/B Ratio	count_in_each_segment
K_means_segments
0	72.399112	5.066225	1.388319	34.620939	53.000000	-14046223.826715	1482212389.891697	3.621029	438533835.667184	23.843656	-3.358948	277
1	50.517273	5.747586	1.130399	31.090909	75.909091	-1072272727.272727	14833090909.090910	4.154545	4298826628.727273	14.803577	-4.552119	11
2	38.099260	-15.370329	2.910500	107.074074	50.037037	-159428481.481481	-3887457740.740741	-9.473704	480398572.845926	90.619220	1.342067	27
3	234.170932	13.400685	1.729989	25.600000	277.640000	1554926560.000000	1572611680.000000	6.045200	578316318.948800	74.960824	14.402452	25

# selecting numerical columns
num_cols = df.select_dtypes(include=np.number).columns.tolist()

plt.figure(figsize=(20, 35))
plt.suptitle("Boxplot of scaled numerical variables for each cluster", fontsize=20)

for i, variable in enumerate(num_cols):
    plt.subplot(4, 3, i + 1)
    sns.boxplot(data=subset_scaled_df, x="K_means_segments", y=variable)

plt.tight_layout(pad=2.0)

Insights

• Cluster 0:

  • 277 companies in this cluster.
  • Price is slightly higher, but mostly in line with clusters 1 and 2.
  • Price changes range about 70 dollars.
  • Moderate volatility.
  • Some high outliers for ROE.
  • Cash Ratio similar to clusters 1 and 2.
  • Tight range of Net Cash Flow between -0.5 and 0.5

• Cluster 1:

  • 11 companies in this cluster.
  • Price is very simlar to cluster 2.
  • Price changes in a very small range between 5 to 15 dollars.
  • Low volatility.
  • Small range for ROE.
  • Cash Ratio similar to cluster 2.
  • Widest range of Net Cash Flow between approximately .4 and -1.2

• Cluster 2:

  • 27 companies in this cluster.
  • Price is very simlar to cluster 1.
  • Large price range between -50 and 10.
  • High volatility
  • Very large outliers for ROE.
  • Cash Ratio similar to cluster 1.
  • Net Cash Flow similar to clusters 0 and 3

• Cluster 3:

  • 25 companies in this cluster.
  • Largest price range.
  • Price change between -5 to 30 dollars.
  • Moderate volatility.
  • Small range for ROE. Similar to cluster 1.
  • Very wide range for Cash Ratio.
  • Net Cash Flow similar to clusters 0 and 2

Hierarchical Clustering

Checking Cophenetic Correlation

df2 = subset_scaled_df.copy()

# list of distance metrics
distance_metrics = ["euclidean", "chebyshev", "mahalanobis", "cityblock"]

# list of linkage methods
linkage_methods = ["single", "complete", "average", "weighted"]

high_cophenet_corr = 0
high_dm_lm = [0, 0]

for dm in distance_metrics:
    for lm in linkage_methods:
        Z = linkage(subset_scaled_df, metric=dm, method=lm)
        c, coph_dists = cophenet(Z, pdist(subset_scaled_df))
        print(
            "Cophenetic correlation for {} distance and {} linkage is {}.".format(
                dm.capitalize(), lm, c
            )
        )
        if high_cophenet_corr < c:
            high_cophenet_corr = c
            high_dm_lm[0] = dm
            high_dm_lm[1] = lm

Cophenetic correlation for Euclidean distance and single linkage is 0.9304469769832865.
Cophenetic correlation for Euclidean distance and complete linkage is 0.8559480642212798.
Cophenetic correlation for Euclidean distance and average linkage is 0.946403836884538.
Cophenetic correlation for Euclidean distance and weighted linkage is 0.7508819056084053.
Cophenetic correlation for Chebyshev distance and single linkage is 0.9161627445317929.
Cophenetic correlation for Chebyshev distance and complete linkage is 0.822502094153258.
Cophenetic correlation for Chebyshev distance and average linkage is 0.9379218754329659.
Cophenetic correlation for Chebyshev distance and weighted linkage is 0.9153206618543516.
Cophenetic correlation for Mahalanobis distance and single linkage is 0.9348505176633238.
Cophenetic correlation for Mahalanobis distance and complete linkage is 0.6881861661402053.
Cophenetic correlation for Mahalanobis distance and average linkage is 0.9360657692078034.
Cophenetic correlation for Mahalanobis distance and weighted linkage is 0.8810701545336992.
Cophenetic correlation for Cityblock distance and single linkage is 0.938373245895409.
Cophenetic correlation for Cityblock distance and complete linkage is 0.8124007660644492.
Cophenetic correlation for Cityblock distance and average linkage is 0.9168123859372297.
Cophenetic correlation for Cityblock distance and weighted linkage is 0.866729262879581.

# printing the combination of distance metric and linkage method with the highest cophenetic correlation
print(
    "Highest cophenetic correlation is {}, which is obtained with {} distance and {} linkage.".format(
        high_cophenet_corr, high_dm_lm[0].capitalize(), high_dm_lm[1]
    )
)

Highest cophenetic correlation is 0.946403836884538, which is obtained with Euclidean distance and average linkage.

Let's explore different linkage methods with Euclidean distance only.

# list of linkage methods
linkage_methods = ["single", "complete", "average", "centroid", "ward", "weighted"]

high_cophenet_corr = 0
high_dm_lm = [0, 0]

for lm in linkage_methods:
    Z = linkage(subset_scaled_df, metric="euclidean", method=lm)
    c, coph_dists = cophenet(Z, pdist(subset_scaled_df))
    print("Cophenetic correlation for {} linkage is {}.".format(lm, c))
    if high_cophenet_corr < c:
        high_cophenet_corr = c
        high_dm_lm[0] = "euclidean"
        high_dm_lm[1] = lm

Cophenetic correlation for single linkage is 0.9304469769832865.
Cophenetic correlation for complete linkage is 0.8559480642212798.
Cophenetic correlation for average linkage is 0.946403836884538.
Cophenetic correlation for centroid linkage is 0.9494262703881242.
Cophenetic correlation for ward linkage is 0.7436374975239648.
Cophenetic correlation for weighted linkage is 0.7508819056084053.

# printing the combination of distance metric and linkage method with the highest cophenetic correlation
print(
    "Highest cophenetic correlation is {}, which is obtained with {} linkage.".format(
        high_cophenet_corr, high_dm_lm[1]
    )
)

Highest cophenetic correlation is 0.9494262703881242, which is obtained with centroid linkage.

Checking Dendrograms

Let's see the dendrograms for the different linkage methods.

# list of linkage methods
linkage_methods = ["single", "complete", "average", "centroid", "ward", "weighted"]

# lists to save results of cophenetic correlation calculation
compare_cols = ["Linkage", "Cophenetic Coefficient"]

# to create a subplot image
fig, axs = plt.subplots(len(linkage_methods), 1, figsize=(15, 30))

# We will enumerate through the list of linkage methods above
# For each linkage method, we will plot the dendrogram and calculate the cophenetic correlation
for i, method in enumerate(linkage_methods):
    Z = linkage(subset_scaled_df, metric="euclidean", method=method)

    dendrogram(Z, ax=axs[i])
    axs[i].set_title(f"Dendrogram ({method.capitalize()} Linkage)")

    coph_corr, coph_dist = cophenet(Z, pdist(subset_scaled_df))
    axs[i].annotate(
        f"Cophenetic\nCorrelation\n{coph_corr:0.2f}",
        (0.80, 0.80),
        xycoords="axes fraction",
    )

Observations

• Highest Cophenetic correlations (correlation and number of clusters): Average (.94 and 13), Centroid (.93 and 11), Single (.92 and 9)

• Centroid or average linkage can be used as they both have similar splits and Cophenetic correlations. The number of clusters to be checked will be at 3, 4, and 5.

• Average linkage will be used since it has the highest Cophenetic correlation score.

Creating Model using sklearn

HCmodel = AgglomerativeClustering(n_clusters=4, affinity="euclidean", linkage="average")
HCmodel.fit(df2)

AgglomerativeClustering(linkage='average', n_clusters=4)

subset_scaled_df["HC_Clusters"] = HCmodel.labels_
df["HC_Clusters"] = HCmodel.labels_

Cluster Profiling

cluster_profile = df.groupby("HC_Clusters").mean()

cluster_profile["count_in_each_segments"] = (
    df.groupby("HC_Clusters")["Security"].count().values
)

cluster_profile.head()

	Current Price	Price Change	Volatility	ROE	Cash Ratio	Net Cash Flow	Net Income	Earnings Per Share	Estimated Shares Outstanding	P/E Ratio	P/B Ratio	K_means_segments	count_in_each_segments
HC_Clusters
0	77.573266	4.148438	1.515708	35.184524	67.154762	6.710469e+07	1.607391e+09	2.90564	5.723178e+08	32.325679	-1.762402	0.386905	336
1	1274.949951	3.190527	1.268340	29.000000	184.000000	-1.671386e+09	2.551360e+09	50.09000	5.093552e+07	25.453183	-1.052429	3.000000	1
2	24.485001	-13.351992	3.482611	802.000000	51.000000	-1.292500e+09	-1.910650e+10	-41.81500	5.195740e+08	60.748608	1.565141	2.000000	2
3	104.660004	16.224320	1.320606	8.000000	958.000000	5.920000e+08	3.669000e+09	1.31000	2.800763e+09	79.893133	5.884467	3.000000	1

# let's see the names of the companies in each cluster
for cl in df["HC_Clusters"].unique():
    print("In cluster {}, the following countries are present:".format(cl))
    print(df[df["HC_Clusters"] == cl]["Security"].unique())
    print()

In cluster 0, the following countries are present:
['American Airlines Group' 'AbbVie' 'Abbott Laboratories'
 'Adobe Systems Inc' 'Analog Devices, Inc.' 'Archer-Daniels-Midland Co'
 'Alliance Data Systems' 'Ameren Corp' 'American Electric Power'
 'AFLAC Inc' 'American International Group, Inc.'
 'Apartment Investment & Mgmt' 'Assurant Inc' 'Arthur J. Gallagher & Co.'
 'Akamai Technologies Inc' 'Albemarle Corp' 'Alaska Air Group Inc'
 'Allstate Corp' 'Allegion' 'Alexion Pharmaceuticals'
 'Applied Materials Inc' 'AMETEK Inc' 'Affiliated Managers Group Inc'
 'Amgen Inc' 'Ameriprise Financial' 'American Tower Corp A'
 'Amazon.com Inc' 'AutoNation Inc' 'Anthem Inc.' 'Aon plc'
 'Anadarko Petroleum Corp' 'Amphenol Corp' 'Arconic Inc'
 'Activision Blizzard' 'AvalonBay Communities, Inc.' 'Broadcom'
 'American Water Works Company Inc' 'American Express Co' 'Boeing Company'
 'Bank of America Corp' 'Baxter International Inc.' 'BB&T Corporation'
 'Bard (C.R.) Inc.' 'Baker Hughes Inc' 'BIOGEN IDEC Inc.'
 'The Bank of New York Mellon Corp.' 'Ball Corp' 'Bristol-Myers Squibb'
 'Boston Scientific' 'BorgWarner' 'Boston Properties' 'Citigroup Inc.'
 'Caterpillar Inc.' 'Chubb Limited' 'CBRE Group'
 'Crown Castle International Corp.' 'Carnival Corp.' 'Celgene Corp.'
 'CF Industries Holdings Inc' 'Citizens Financial Group' 'Church & Dwight'
 'C. H. Robinson Worldwide' 'Charter Communications' 'CIGNA Corp.'
 'Cincinnati Financial' 'Colgate-Palmolive' 'Comerica Inc.'
 'CME Group Inc.' 'Chipotle Mexican Grill' 'Cummins Inc.' 'CMS Energy'
 'Centene Corporation' 'CenterPoint Energy' 'Capital One Financial'
 'Cabot Oil & Gas' 'The Cooper Companies' 'CSX Corp.' 'CenturyLink Inc'
 'Cognizant Technology Solutions' 'Citrix Systems' 'CVS Health'
 'Chevron Corp.' 'Concho Resources' 'Dominion Resources' 'Delta Air Lines'
 'Du Pont (E.I.)' 'Deere & Co.' 'Discover Financial Services'
 'Quest Diagnostics' 'Danaher Corp.' 'The Walt Disney Company'
 'Discovery Communications-A' 'Discovery Communications-C'
 'Delphi Automotive' 'Digital Realty Trust' 'Dun & Bradstreet'
 'Dover Corp.' 'Dr Pepper Snapple Group' 'Duke Energy' 'DaVita Inc.'
 'Devon Energy Corp.' 'eBay Inc.' 'Ecolab Inc.' 'Consolidated Edison'
 'Equifax Inc.' "Edison Int'l" 'Eastman Chemical' 'EOG Resources'
 'Equinix' 'Equity Residential' 'EQT Corporation' 'Eversource Energy'
 'Essex Property Trust, Inc.' 'E*Trade' 'Eaton Corporation'
 'Entergy Corp.' 'Edwards Lifesciences' 'Exelon Corp.' "Expeditors Int'l"
 'Expedia Inc.' 'Extra Space Storage' 'Ford Motor' 'Fastenal Co'
 'Fortune Brands Home & Security' 'Freeport-McMoran Cp & Gld'
 'FirstEnergy Corp' 'Fidelity National Information Services' 'Fiserv Inc'
 'FLIR Systems' 'Fluor Corp.' 'Flowserve Corporation' 'FMC Corporation'
 'Federal Realty Investment Trust' 'First Solar Inc'
 'Frontier Communications' 'General Dynamics'
 'General Growth Properties Inc.' 'Gilead Sciences' 'Corning Inc.'
 'General Motors' 'Genuine Parts' 'Garmin Ltd.' 'Goodyear Tire & Rubber'
 'Grainger (W.W.) Inc.' 'Halliburton Co.' 'Hasbro Inc.'
 'Huntington Bancshares' 'HCA Holdings' 'Welltower Inc.' 'HCP Inc.'
 'Hess Corporation' 'Hartford Financial Svc.Gp.' 'Harley-Davidson'
 "Honeywell Int'l Inc." 'Hewlett Packard Enterprise' 'HP Inc.'
 'Hormel Foods Corp.' 'Henry Schein' 'Host Hotels & Resorts'
 'The Hershey Company' 'Humana Inc.' 'International Business Machines'
 'IDEXX Laboratories' 'Intl Flavors & Fragrances' 'Intel Corp.'
 'International Paper' 'Interpublic Group' 'Iron Mountain Incorporated'
 'Intuitive Surgical Inc.' 'Illinois Tool Works' 'Invesco Ltd.'
 'J. B. Hunt Transport Services' 'Jacobs Engineering Group'
 'Juniper Networks' 'JPMorgan Chase & Co.' 'Kimco Realty' 'Kimberly-Clark'
 'Kinder Morgan' 'Coca Cola Company' 'Kansas City Southern'
 'Leggett & Platt' 'Lennar Corp.' 'Laboratory Corp. of America Holding'
 'LKQ Corporation' 'L-3 Communications Holdings' 'Lilly (Eli) & Co.'
 'Lockheed Martin Corp.' 'Alliant Energy Corp' 'Leucadia National Corp.'
 'Southwest Airlines' 'Level 3 Communications' 'LyondellBasell'
 'Mastercard Inc.' 'Mid-America Apartments' 'Macerich' "Marriott Int'l."
 'Masco Corp.' 'Mattel Inc.' "McDonald's Corp." "Moody's Corp"
 'Mondelez International' 'MetLife Inc.' 'Mohawk Industries'
 'Mead Johnson' 'McCormick & Co.' 'Martin Marietta Materials'
 'Marsh & McLennan' '3M Company' 'Monster Beverage' 'Altria Group Inc'
 'The Mosaic Company' 'Marathon Petroleum' 'Merck & Co.'
 'Marathon Oil Corp.' 'M&T Bank Corp.' 'Mettler Toledo' 'Murphy Oil'
 'Mylan N.V.' 'Navient' 'Noble Energy Inc' 'NASDAQ OMX Group'
 'NextEra Energy' 'Newmont Mining Corp. (Hldg. Co.)' 'Netflix Inc.'
 'Newfield Exploration Co' 'Nielsen Holdings'
 'National Oilwell Varco Inc.' 'Norfolk Southern Corp.'
 'Northern Trust Corp.' 'Nucor Corp.' 'Newell Brands'
 'Realty Income Corporation' 'ONEOK' 'Omnicom Group' "O'Reilly Automotive"
 'Occidental Petroleum' "People's United Financial" 'Pitney-Bowes'
 'PACCAR Inc.' 'PG&E Corp.' 'Public Serv. Enterprise Inc.' 'PepsiCo Inc.'
 'Pfizer Inc.' 'Principal Financial Group' 'Procter & Gamble'
 'Progressive Corp.' 'Pulte Homes Inc.' 'Philip Morris International'
 'PNC Financial Services' 'Pentair Ltd.' 'Pinnacle West Capital'
 'PPG Industries' 'PPL Corp.' 'Prudential Financial' 'Phillips 66'
 'Quanta Services Inc.' 'Praxair Inc.' 'PayPal' 'Ryder System'
 'Royal Caribbean Cruises Ltd' 'Regeneron' 'Robert Half International'
 'Roper Industries' 'Range Resources Corp.' 'Republic Services Inc'
 'SCANA Corp' 'Charles Schwab Corporation' 'Spectra Energy Corp.'
 'Sealed Air' 'Sherwin-Williams' 'SL Green Realty'
 'Scripps Networks Interactive Inc.' 'Southern Co.'
 'Simon Property Group Inc' 'S&P Global, Inc.' 'Stericycle Inc'
 'Sempra Energy' 'SunTrust Banks' 'State Street Corp.'
 'Skyworks Solutions' 'Southwestern Energy' 'Synchrony Financial'
 'Stryker Corp.' 'AT&T Inc' 'Molson Coors Brewing Company'
 'Teradata Corp.' 'Tegna, Inc.' 'Torchmark Corp.'
 'Thermo Fisher Scientific' 'TripAdvisor' 'The Travelers Companies Inc.'
 'Tractor Supply Company' 'Tyson Foods' 'Tesoro Petroleum Co.'
 'Total System Services' 'Texas Instruments' 'Under Armour'
 'United Continental Holdings' 'UDR Inc' 'Universal Health Services, Inc.'
 'United Health Group Inc.' 'Unum Group' 'Union Pacific'
 'United Parcel Service' 'United Technologies' 'Varian Medical Systems'
 'Valero Energy' 'Vulcan Materials' 'Vornado Realty Trust'
 'Verisk Analytics' 'Verisign Inc.' 'Vertex Pharmaceuticals Inc'
 'Ventas Inc' 'Verizon Communications' 'Waters Corporation'
 'Wec Energy Group Inc' 'Wells Fargo' 'Whirlpool Corp.'
 'Waste Management Inc.' 'Williams Cos.' 'Western Union Co'
 'Weyerhaeuser Corp.' 'Wyndham Worldwide' 'Wynn Resorts Ltd'
 'Cimarex Energy' 'Xcel Energy Inc' 'XL Capital' 'Exxon Mobil Corp.'
 'Dentsply Sirona' 'Xerox Corp.' 'Xylem Inc.' 'Yahoo Inc.'
 'Yum! Brands Inc' 'Zimmer Biomet Holdings' 'Zions Bancorp' 'Zoetis']

In cluster 2, the following countries are present:
['Apache Corporation' 'Chesapeake Energy']

In cluster 3, the following countries are present:
['Facebook']

In cluster 1, the following countries are present:
['Priceline.com Inc']

Creating Final Model

We will use Ward linkage to see if we can make the clusters more distinct from each other.

HCmodel = AgglomerativeClustering(n_clusters=4, affinity="euclidean", linkage="ward")
HCmodel.fit(subset_scaled_df)

AgglomerativeClustering(n_clusters=4)

subset_scaled_df["HC_Clusters"] = HCmodel.labels_
df["HC_Clusters"] = HCmodel.labels_

Cluster Profiling

cluster_profile = df.groupby("HC_Clusters").mean()

cluster_profile["count_in_each_segments"] = (
    df.groupby("HC_Clusters")["Security"].count().values
)

# let's see the names of the companies in each cluster
for cl in df["HC_Clusters"].unique():
    print(
        "The",
        df[df["HC_Clusters"] == cl]["Security"].nunique(),
        "countries in cluster",
        cl,
        "are:",
    )
    print(df[df["HC_Clusters"] == cl]["Security"].unique())
    print("-" * 100, "\n")

The 273 countries in cluster 3 are:
['American Airlines Group' 'AbbVie' 'Abbott Laboratories'
 'Adobe Systems Inc' 'Archer-Daniels-Midland Co' 'Ameren Corp'
 'American Electric Power' 'AFLAC Inc'
 'American International Group, Inc.' 'Apartment Investment & Mgmt'
 'Assurant Inc' 'Arthur J. Gallagher & Co.' 'Akamai Technologies Inc'
 'Albemarle Corp' 'Alaska Air Group Inc' 'Allstate Corp'
 'Applied Materials Inc' 'AMETEK Inc' 'Affiliated Managers Group Inc'
 'Ameriprise Financial' 'American Tower Corp A' 'AutoNation Inc'
 'Anthem Inc.' 'Aon plc' 'Amphenol Corp' 'Arconic Inc'
 'Activision Blizzard' 'AvalonBay Communities, Inc.' 'Broadcom'
 'American Water Works Company Inc' 'American Express Co' 'Boeing Company'
 'Baxter International Inc.' 'BB&T Corporation' 'Bard (C.R.) Inc.'
 'The Bank of New York Mellon Corp.' 'Ball Corp' 'Bristol-Myers Squibb'
 'Boston Scientific' 'BorgWarner' 'Boston Properties' 'Caterpillar Inc.'
 'Chubb Limited' 'CBRE Group' 'Crown Castle International Corp.'
 'Carnival Corp.' 'CF Industries Holdings Inc' 'Citizens Financial Group'
 'Church & Dwight' 'C. H. Robinson Worldwide' 'CIGNA Corp.'
 'Cincinnati Financial' 'Comerica Inc.' 'CME Group Inc.' 'Cummins Inc.'
 'CMS Energy' 'Centene Corporation' 'CenterPoint Energy'
 'Capital One Financial' 'The Cooper Companies' 'CSX Corp.'
 'CenturyLink Inc' 'Cognizant Technology Solutions' 'Citrix Systems'
 'CVS Health' 'Chevron Corp.' 'Dominion Resources' 'Delta Air Lines'
 'Du Pont (E.I.)' 'Deere & Co.' 'Discover Financial Services'
 'Quest Diagnostics' 'Danaher Corp.' 'The Walt Disney Company'
 'Discovery Communications-A' 'Discovery Communications-C'
 'Delphi Automotive' 'Digital Realty Trust' 'Dun & Bradstreet'
 'Dover Corp.' 'Dr Pepper Snapple Group' 'Duke Energy' 'DaVita Inc.'
 'eBay Inc.' 'Ecolab Inc.' 'Consolidated Edison' 'Equifax Inc.'
 "Edison Int'l" 'Eastman Chemical' 'Equity Residential'
 'Eversource Energy' 'Essex Property Trust, Inc.' 'E*Trade'
 'Eaton Corporation' 'Entergy Corp.' 'Exelon Corp.' "Expeditors Int'l"
 'Expedia Inc.' 'Extra Space Storage' 'Fastenal Co'
 'Fortune Brands Home & Security' 'FirstEnergy Corp'
 'Fidelity National Information Services' 'Fiserv Inc' 'FLIR Systems'
 'Fluor Corp.' 'Flowserve Corporation' 'FMC Corporation'
 'Federal Realty Investment Trust' 'General Dynamics'
 'General Growth Properties Inc.' 'Gilead Sciences' 'Corning Inc.'
 'General Motors' 'Genuine Parts' 'Garmin Ltd.' 'Goodyear Tire & Rubber'
 'Grainger (W.W.) Inc.' 'Hasbro Inc.' 'Huntington Bancshares'
 'HCA Holdings' 'Welltower Inc.' 'HCP Inc.' 'Hartford Financial Svc.Gp.'
 'Harley-Davidson' "Honeywell Int'l Inc." 'HP Inc.' 'Hormel Foods Corp.'
 'Henry Schein' 'Host Hotels & Resorts' 'The Hershey Company'
 'Humana Inc.' 'International Business Machines' 'IDEXX Laboratories'
 'Intl Flavors & Fragrances' 'International Paper' 'Interpublic Group'
 'Iron Mountain Incorporated' 'Illinois Tool Works' 'Invesco Ltd.'
 'J. B. Hunt Transport Services' 'Jacobs Engineering Group'
 'Juniper Networks' 'Kimco Realty' 'Kansas City Southern'
 'Leggett & Platt' 'Lennar Corp.' 'Laboratory Corp. of America Holding'
 'LKQ Corporation' 'L-3 Communications Holdings' 'Lilly (Eli) & Co.'
 'Lockheed Martin Corp.' 'Alliant Energy Corp' 'Leucadia National Corp.'
 'Southwest Airlines' 'Level 3 Communications' 'LyondellBasell'
 'Mastercard Inc.' 'Mid-America Apartments' 'Macerich' "Marriott Int'l."
 'Masco Corp.' 'Mattel Inc.' "Moody's Corp" 'Mondelez International'
 'MetLife Inc.' 'Mohawk Industries' 'Mead Johnson' 'McCormick & Co.'
 'Martin Marietta Materials' 'Marsh & McLennan' '3M Company'
 'Altria Group Inc' 'The Mosaic Company' 'Marathon Petroleum'
 'Merck & Co.' 'M&T Bank Corp.' 'Mettler Toledo' 'Mylan N.V.' 'Navient'
 'NASDAQ OMX Group' 'NextEra Energy' 'Newmont Mining Corp. (Hldg. Co.)'
 'Nielsen Holdings' 'Norfolk Southern Corp.' 'Northern Trust Corp.'
 'Nucor Corp.' 'Newell Brands' 'Realty Income Corporation' 'Omnicom Group'
 "O'Reilly Automotive" "People's United Financial" 'Pitney-Bowes'
 'PACCAR Inc.' 'PG&E Corp.' 'Public Serv. Enterprise Inc.' 'PepsiCo Inc.'
 'Principal Financial Group' 'Procter & Gamble' 'Progressive Corp.'
 'Pulte Homes Inc.' 'Philip Morris International' 'PNC Financial Services'
 'Pentair Ltd.' 'Pinnacle West Capital' 'PPG Industries' 'PPL Corp.'
 'Prudential Financial' 'Phillips 66' 'Praxair Inc.' 'PayPal'
 'Ryder System' 'Royal Caribbean Cruises Ltd' 'Robert Half International'
 'Roper Industries' 'Republic Services Inc' 'SCANA Corp'
 'Charles Schwab Corporation' 'Spectra Energy Corp.' 'Sealed Air'
 'Sherwin-Williams' 'SL Green Realty' 'Scripps Networks Interactive Inc.'
 'Southern Co.' 'Simon Property Group Inc' 'Stericycle Inc'
 'Sempra Energy' 'SunTrust Banks' 'State Street Corp.'
 'Skyworks Solutions' 'Synchrony Financial' 'Stryker Corp.'
 'Molson Coors Brewing Company' 'Tegna, Inc.' 'Torchmark Corp.'
 'Thermo Fisher Scientific' 'The Travelers Companies Inc.'
 'Tractor Supply Company' 'Tyson Foods' 'Tesoro Petroleum Co.'
 'Total System Services' 'Texas Instruments' 'Under Armour'
 'United Continental Holdings' 'UDR Inc' 'Universal Health Services, Inc.'
 'United Health Group Inc.' 'Unum Group' 'Union Pacific'
 'United Parcel Service' 'United Technologies' 'Varian Medical Systems'
 'Valero Energy' 'Vulcan Materials' 'Vornado Realty Trust'
 'Verisk Analytics' 'Verisign Inc.' 'Ventas Inc' 'Wec Energy Group Inc'
 'Whirlpool Corp.' 'Waste Management Inc.' 'Western Union Co'
 'Weyerhaeuser Corp.' 'Wyndham Worldwide' 'Xcel Energy Inc' 'XL Capital'
 'Dentsply Sirona' 'Xerox Corp.' 'Xylem Inc.' 'Yum! Brands Inc'
 'Zimmer Biomet Holdings' 'Zions Bancorp' 'Zoetis']
---------------------------------------------------------------------------------------------------- 

The 24 countries in cluster 2 are:
['Analog Devices, Inc.' 'Alliance Data Systems' 'Alexion Pharmaceuticals'
 'Amgen Inc' 'Amazon.com Inc' 'BIOGEN IDEC Inc.' 'Celgene Corp.'
 'Chipotle Mexican Grill' 'Equinix' 'Edwards Lifesciences' 'Facebook'
 'First Solar Inc' 'Frontier Communications' 'Intuitive Surgical Inc.'
 "McDonald's Corp." 'Monster Beverage' 'Netflix Inc.' 'Priceline.com Inc'
 'Regeneron' 'TripAdvisor' 'Vertex Pharmaceuticals Inc'
 'Waters Corporation' 'Wynn Resorts Ltd' 'Yahoo Inc.']
---------------------------------------------------------------------------------------------------- 

The 32 countries in cluster 0 are:
['Allegion' 'Apache Corporation' 'Anadarko Petroleum Corp'
 'Baker Hughes Inc' 'Chesapeake Energy' 'Charter Communications'
 'Colgate-Palmolive' 'Cabot Oil & Gas' 'Concho Resources'
 'Devon Energy Corp.' 'EOG Resources' 'EQT Corporation'
 'Freeport-McMoran Cp & Gld' 'Halliburton Co.' 'Hess Corporation'
 'Hewlett Packard Enterprise' 'Kimberly-Clark' 'Kinder Morgan'
 'Marathon Oil Corp.' 'Murphy Oil' 'Noble Energy Inc'
 'Newfield Exploration Co' 'National Oilwell Varco Inc.' 'ONEOK'
 'Occidental Petroleum' 'Quanta Services Inc.' 'Range Resources Corp.'
 'S&P Global, Inc.' 'Southwestern Energy' 'Teradata Corp.' 'Williams Cos.'
 'Cimarex Energy']
---------------------------------------------------------------------------------------------------- 

The 11 countries in cluster 1 are:
['Bank of America Corp' 'Citigroup Inc.' 'Ford Motor' 'Intel Corp.'
 'JPMorgan Chase & Co.' 'Coca Cola Company' 'Pfizer Inc.' 'AT&T Inc'
 'Verizon Communications' 'Wells Fargo' 'Exxon Mobil Corp.']
---------------------------------------------------------------------------------------------------- 

# lets display cluster profile
cluster_profile.style.highlight_max(color="lightgreen", axis=0)

	Current Price	Price Change	Volatility	ROE	Cash Ratio	Net Cash Flow	Net Income	Earnings Per Share	Estimated Shares Outstanding	P/E Ratio	P/B Ratio	K_means_segments	count_in_each_segments
HC_Clusters
0	46.558126	-11.798670	2.617878	178.750000	50.250000	43497156.250000	-3197471875.000000	-7.785312	473289495.126250	72.496532	-0.780467	1.718750	32
1	42.848182	6.270446	1.123547	22.727273	71.454545	558636363.636364	14631272727.272728	3.410000	4242572567.290909	15.242169	-4.924615	1.181818	11
2	246.574304	14.284326	1.769621	26.500000	279.916667	459120250.000000	1009205541.666667	6.167917	549432140.538333	90.097512	14.081386	2.958333	24
3	71.846974	4.953643	1.392784	25.117216	53.831502	1197787.545788	1557673743.589744	3.691044	443918320.070366	23.583804	-3.087957	0.003663	273

plt.figure(figsize=(20, 35))
plt.suptitle("Boxplot of scaled numerical variables for each cluster", fontsize=20)

for i, variable in enumerate(num_cols):
    plt.subplot(4, 3, i + 1)
    sns.boxplot(data=subset_scaled_df, x="HC_Clusters", y=variable)

plt.tight_layout(pad=2.0)

Insights

• Cluster 0:

  • 32 companies in this cluster.
  • High volatility and ROE.

• Cluster 1:

  • 11 companies in this cluster.
  • Highest Net Cash Flow, Net Income and Estimated Shares Outstanding.

• Cluster 2:

  • 24 companies in this cluster.
  • Highest current price, price change, Cash Ratio, Earnings Per Share, P/E Ratio and P/B Ratio.

• Cluster 3:

  • 273 companies in this cluster.
  • Moderate values compared to other clusters across variables.

K-means vs Hierarchical Clustering

• Processing time was approximately equal.
• The clustering techniques both yielded similar results. Use of the Ward linkage gave slightly more distinct clusters.
• The observations in each cluster remained relatively the same between the two techniques.
• Four clusters was the appropriate number of clusters from both algorithms.

Actionable Insights and Recommendations

Cluster 0:

• These are high volatility companies characterized by low/negative cash and earnings per share.

Cluster 1:

• Low volatility companies with a fair amount of cash. Many of these companies would be consider value stocks.

Cluster 2:

• Companies that may be in transition from earlier growth stages. Some very high P/E, but low ROE indicating many of these company's stocks are overvalued in the marketplace.

Cluster 3:

• Low ROE and cash flows. Low P/E's indicating possible early buying opportunties for companies on the rebound.

This model provides four clusters each with their own attributes based on the stocks within the clusters. Selecting some stocks from each of the clusters could provide diversification for a client's portfolio. However, stock selection still needs to be done by thoroughly researching and valuing recommendations on a company-by-company basis. Randomly selecting stocks by taking a few from each cluster will not necessarily benefit the client or meet the Trade&Ahead's financial due diligence on behalf of their client. The clusters should be considered as a guideline for a client's overall portfolio as Trade&Ahead's investment research team uncovers potential stock investment opportunties.